The slightly modified constructs in
BlockSim FTI erase
the distinction between reliability block diagrams (RBD) and fault trees.
Given this, any analysis that is possible in a BlockSim RBD (including
throughput analysis) is also available when utilizing fault trees. In this
article, the simulation of an RBD and its corresponding fault tree will be
compared.

Example

Consider the RBD shown in Figure 1 and its
equivalent fault tree representation in Figure 2.

Figure 1: RBD for a repairable system

Figure 2: Fault tree equivalent for the RBD
shown in Figure 1

In addition, assume the following basic
failure and repair properties for each block and event:

Block A

Failure Distribution: Weibull; β =
1.5; η
= 1,000.

Corrective Distribution: Weibull;
β
= 1.5; η
= 100.

Block B

Failure Distribution: Exponential;
μ
= 10,000.

Corrective Distribution: Weibull;
β
= 1.5; η
= 20.

Block C

Failure Distribution: Normal; μ =
1,000; σ = 200.

Corrective Distribution: Normal;
μ = 6; σ = 2.

Block D

Failure Distribution: Weibull; β =
1.5; η
= 10,000.

Corrective Distribution: Exponential;
μ = 10.

Block E

Failure Distribution: Weibull; β =
3; η
= 1,000.

Corrective Distribution: Weibull;
β
= 1.5; η
= 20.

Block F

Failure Distribution: Weibull; β =
1.5; η
= 5,000.

Corrective Distribution: Weibull;
β
= 1.5; η
= 100.

Block G

Failure Distribution: Exponential;
μ
= 100,000.

Corrective Distribution: Weibull;
β
= 1.5; η
= 10.

Block H

Failure Distribution: Normal; μ =
5,000; σ= 50.

Corrective Distribution: Normal;
μ = 10; σ =
2.

Figure 3 shows a sample table of simulation
results for up to t = 1,000 using simulations for each diagram and an
identical seed.

Figure 3: Sample simulation results

As expected, the results are equivalent (within
an expected difference due to simulation) regardless of the diagram type
used. It should be pointed out that even though the same seed was utilized
by both diagrams, the results are not always expected to be identical. The
order in which the blocks are read from a fault tree diagram during the
simulation may differ from the order in which they are read in the RBD.
Therefore, a different random number stream for each block (e.g.
block G in the RBD may receive a different sequence of random numbers than
event block G in the FTI) may be utilized.